On 20 February 2021, he scored his first goal for Dynamo in a 2–0 victory over Spartak Moscow in a Russian Cup game.[4]
On 18 March 2021, he came on as a substitute in the 55th minute in the away game against Krasnodar, with Dynamo down 0–2. 11 minutes later he scored his first RPL goal for Dynamo that equalized the score, and in the 81st minute he scored the winning goal that established the final score of 3–2 for Dynamo. He was selected as player of the match.[5] In Dynamo's next league game on 3 April 2021 against Ufa, Tyukavin scored a goal, assisted on another, and another Dynamo goal was scored on a rebound tap-in after the ball hit the goalpost after Tyukavin's header, as Dynamo won 4–0. He was selected as player of the match again. In the next game on 11 April 2021 against Ural Yekaterinburg, he assisted on both Dynamo goals in a 2–2 draw. Dynamo fans voted him Player of the Month for April 2021.[6]
On 18 June 2021, he extended his contract with Dynamo for 3 additional seasons with an option for another season.[7]
On 20 August 2022, Tyukavin scored the only goal of the game in an oldest Russian derby game against Spartak Moscow, securing the first Dynamo home league victory in this derby since 2008.[8][9] He was selected as Player of the Month by Dynamo fans for May/June 2023.[10] He was voted as Player of the Season for the 2022–23 season by the fans.[11]
On 1 December 2023, he extended his Dynamo contract to summer 2028.[12] He was selected as player of the month for November and December 2023 games by Dynamo fans and by the Russian Premier League.[13][14] He was selected as player of the month for the second time in the season for April 2024 games.[15][16]
On 26 May 2024, Tyukavin was named by the league as player of the season, forward of the season and his backheel rabona goal against Sochi on 5 May 2024 was named goal of the season.[17] He was also voted Dynamo player of the month for May.[18] On 12 June 2024, he was chosen as Footballer of the Year in Russia in a traditional poll taken among the league players.[19]
He was called up to the Russia national football team for the first time for World Cup qualifiers against Croatia, Cyprus and Malta in September 2021.[21] He made his debut on 4 September 2021 against Cyprus, substituting Fyodor Smolov in the 75th minute of a 2–0 away victory.[22]